Problem: Solve for $x$ and $y$ by deriving an expression for $y$ from the second equation, and substituting it back into the first equation. $\begin{align*}6x+5y &= -8 \\ -2x+y &= -8\end{align*}$
Solution: Begin by moving the $x$ -term in the second equation to the right side of the equation. $y = {2x-8}$ Substitute this expression for $y$ in the first equation. $6x+5({2x - 8}) = -8$ $6x + 10x - 40 = -8$ Simplify by combining terms, then solve for $x$ $16x - 40 = -8$ $16x = 32$ $x = 2$ Substitute $2$ for $x$ back into the top equation. $6( 2)+5y = -8$ $12+5y = -8$ $5y = -20$ $y = -4$ The solution is $\enspace x = 2, \enspace y = -4$.